Every graph on n vertices with minimum degree at least ((7+sqrt(21))/14)n admits a fractional triangle decomposition, improving prior bounds.
Dukes, Rational decomposition of dense hypergraphs and so me related eigenvalue estimates, Linear Algebra and Its Applications , 436(9), 2012, 3736–3746
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Progress towards Nash-Williams' Conjecture on Triangle Decompositions
Every graph on n vertices with minimum degree at least ((7+sqrt(21))/14)n admits a fractional triangle decomposition, improving prior bounds.